Modelling of the Plastic Behavior of Cu Crystal with Twinning-Induced Softening and Strengthening Effects

doi:10.11900/0412.1961.2021.00230

Acta Metall Sin

2022, Vol. 58

Issue (3): 375-384 DOI: 10.11900/0412.1961.2021.00230

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Modelling of the Plastic Behavior of Cu Crystal with Twinning-Induced Softening and Strengthening Effects

GUO Xiangru¹^,², SHEN Junjie¹^,²(

)

^1.Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin 300384, China
^2.National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, China

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GUO Xiangru, SHEN Junjie. Modelling of the Plastic Behavior of Cu Crystal with Twinning-Induced Softening and Strengthening Effects. Acta Metall Sin, 2022, 58(3): 375-384.

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Abstract

Dislocation slip and twinning are the main deformation mechanisms dominating plastic behavior of crystalline materials, such as twinning-induced plasticity steel, Cu, Mg, and their alloys. The influence of twinning and interaction between dislocations and twins on the plastic deformation of crystal materials is complex. On the one hand, a sudden stress drop in the stress-strain curve during twin nucleation, propagation, and growth (TNPG) of crystal materials, i.e., the twinning softening effect, is evident. On the other hand, the interaction between twins and dislocations demonstrates the strengthening effect of plastic deformation. Polycrystalline materials are used in engineering applications, and twin nucleation corresponds to different strains in each grain. Therefore, determining the influence of twin softening and strengthening effects on plastic deformation of polycrystalline materials is difficult. In this work, a crystal plastic finite element model of Cu, considering the twinning softening effect, was developed to describe the TNPG process based on the crystal plasticity theory. The method was used to reveal the influence of twins' activation and their interaction with dislocations on strain hardening during the tension of Cu single crystal and polycrystal. The results show that twinning has an evident orientation effect. Under twinning favorable orientation, a sudden stress drop in the stress-strain curve caused by twinning propagation during plastic deformation of Cu single crystal is evident, and the total plastic deformation can be divided into three stages: slip, twinning, and interaction between dislocations and twins. Compared with Cu single crystal, the stress-strain curve changes smoothly and the strain hardening rate is higher during the tension of Cu polycrystal. Meanwhile, the dislocation density is concentrated at the grain boundary, and twins are easy to form at the grain boundary during the plastic deformation of Cu polycrystal.

Key words: crystal plasticity twining softening orientation effect strain hardening plastic deformation

Received: 27 May 2021

ZTFLH:

TG146.1

Fund: National Natural Science Foundation of China(52105393);Natural Science Foundation of Tianjin(18JCYBJC88700)

About author: SHEN Junjie, associate professor, Tel: (022)60214133, E-mail: sjj1982428@sina.com

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https://www.ams.org.cn/EN/10.11900/0412.1961.2021.00230 OR https://www.ams.org.cn/EN/Y2022/V58/I3/375

Fig.1 Schematic of macroscopic tensile process for Cu single crystal by using crystal plastic finite element (CPFE) model (Uz—the tensile direction)

Parameter	Value	Unit
C₁₁^[28]	168	GPa
C₁₂^[28]	121	GPa
C₄₄^[28]	75	GPa
$f t$ ^[2,31]	0.7
$γ ˙ 0$ ^[29,30]	0.001	s^-1
$m$ ^[29,30]	0.024
$s 0$ ^[29,30]	5	MPa
$μ$ ^[28]	48	GPa
b^[28]	0.025	nm
$ρ 0$ ^[29,30]	10¹²	m^-2
$k r$ ^[29,30]	6
$k f$ ^[29,30]	0.3
$e$ ^[2,31]	220	nm
D^[2,31]	3	mm
$s 0, β$	150	MPa
$s 1, β$	60	MPa
$s g, β$	110	MPa
$f g, β$ ^[23]	0.005
$h 0, β$ ^[23]	70
$h 1, β$ ^[23]	0

Table 1 Material parameters in the CPFE model for Cu single crystal^[2,23,28-31]

Fig.2 Simulated and experimental^[2,28] results of true stress and twin volume fraction (TVF) of Cu single crystal along [541] and [163] orientations, respectively

Fig.3 Slip activities of slip systems (a) and twinning activities of twin systems (b) during the tension of Cu single crystal along the [541] orientation (The inset shows the enlarged view of the rectangle area in Fig.3a)

Fig.4 Evolution curves of true stress, strain hardening rate, and dislocation density of Cu single crystal with different twin volume fraction saturation values along [541] orientation during tension

Fig.5 Schematic of macroscopic tensile process for Cu polycrystal by using CPFE model (The illustration on the right shows the morphology of a representative grain)

Fig.6 Evolution curves of true stress, dislocation density, and TVF of Cu polycrystal during tension

Fig.7 Evolution curves of strain hardening rate of Cu single crystal with different orientations and polycrystal during tension

Fig.8 Distribution maps of dislocation density (a) and TVF (b) of Cu polycrystal after tension (The dashed circles in Fig.8a mark the locations of dislocation density concentration)

Fig.9 Distributions of TVF at different strains (ε) of Cu polycrystal during tension

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